COMPULSORY MATHS
Model Set 1
Time: 3.00 hours Full Marks: 100
Pass Marks: 32
(Group ‘A’) [9×(2+2)=36]
1. a. (Evaluate):
b. (Simplify):
2. a. (Solve) :
b.
If 7 is subtracted from the square of a positive number, the result is 9. Find the number.
3. a.
If = 400+20a ,=18+2a, and the mean of the given series is 20, find the value of a.
b.
Find the median class and value of median from the adjoining cumulative frequency curve.
4. a.
A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting such card is queen or a black ace.
b.
A coin is tossed two times and represents the probabilities in a tree diagram.
5. a.
In ∆ABC, AB=8 cm, BC= 12 cm and ÐABC=60°.
Find the area of the triangle.
b.
The adjoining diagram is a triangular based solid prism. If AB= 3 cm, BC=5 cm and CF= 12 cm find the volume of the prism.
6. a .
If the sum of radius and height of cylinder is 12 cm and circumference of base is 416 cm find the total surface area of that cylinder.
b.
The diagram given alongside is of a solid sphere. If AB= 28 cm, Find the volume of the sphere.
7. a.
The marked price of an article was fixed to Rs. 2760 by increasing 15% in its actual price. Find its actual price.
b.
Find the compound amount on Rs. 5000 in 2 years at 10% per annum.
8. a.
If the given figure, WXYZ is a parallelogram . WX is extended up to U and ∆ZYU is formed. If Area of ∆ZYU is 15cm2, find the area of ∆WXT.
9. a.
In the given figure, points A, D, C and B are on semi-circle. If ÐDAC=30° and ÐABC= 70°, find ÐACD.
b
In the given figure, PT touches a circle at a point A. If ÐBAT=60° and ÐBAC=50°, find ÐABC.
;d'x …vÚ (Group ‘B’) [16×4=36]
10
In a survey of the group of students, it was found that 70% of students studied about scientists, 65% about players and 430 studied about both scientists and players. If 8% did not study about scientists and players, then,
i)
Find the total number of students who took part in the survey.
11. . (Find the H.C.F of):
and
12. . (Solve) : 5x-1 + 5-x = 1
13. (Simplify):-
14.
A two digit number is four times the sum of its digits. If the sum of the number formed by reversing its digits and 9 is two times the original number, find the original number.
15.
If the mean of the following data is 68, find the value of x.
Marks obtained
40-50
50-60
60-70
70-80
80-90
90-100
No.of students
17
22
28
26
x
12
16.
The angle of elevation of the top of a tree, 40m high situated at the bank of a river when observed from the opposite bank of the river is found to be 30°, find the breadth of the river.
17.
The given solid object is made up of a cylinder and a hemisphere whose diameter of the base is 14 cm and total length is 21 cm. Find the total surface area of the solid object.
18.
Find the total surface area of the following
square based pyramid.
19.
A and B can do a piece of work in 12 and 16 days respectively. A and B work together for 4 days and B leaves the work, find how long will A take to complete the remaining work.
20.
A camera was sold after allowing 25% discount on the marked price and then levying 10% value added tax (VAT). If the discounted amount was Rs.750, how much value added tax (VAT) was levied on the price of the camera?
21.
The population of a village increases every year by 5%. If 1025 people leave the village at the end of two years and the population of the village is 10,000, find the population of the village in the beginning.
22.
Prove that the triangles PQR and SQR standing on same base QR and between same parallel lines QR and PS are equal in area.
23.
In alongside diagram, PT is the diameter and O is centre of circle. If arc SR=arc RT, prove that PS//OR.
24. Verify experimentally that the angles at the circumference standing on the same arc of a circle are equal.(Two circles of radii at least 3 cm are necessary.)
25.
Construct a quadrilateral ABCD in which AB=5.8cm, BC=6.2cm , CD=5.1cm , DA=4.8cm and ÐBAD=60°.also construct a triangle equal in area to the quadrilateral ABCD.
SORRY DUE TO SOME PROBLEMS WE CANT SHOW ALL THE INFORMATIONS.
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